Question: Solve for $b$. $-11b+7 = 40$ $b =$
Explanation: Let's subtract and then divide to get $b$ by itself. $\begin{aligned} -11b+7 &= 40 \\ \\ -11b+7 {-7}&= 40{-7}~~~~{\text{subtract }7} \text{ from each side}\\ \\ -11b+\cancel{ 7} {{-}\cancel{{7}}}&= 40{-7}\\ \\ -11b &=40{-7}\end{aligned}$ $\begin{aligned}-11b &= 33 \\ \\ \dfrac{-11b}{{-11}} &= \dfrac{33}{{-11}} ~~~~~~~\text{divide each side by } {-11} \text{ to get } b \text{ by itself }\\ \\ \dfrac{\cancel{-11}b}{\cancel{{-11}}} &= \dfrac{33}{{-11}} \\ \\ b &= \dfrac{33}{{-11}} \end{aligned}$ The answer: $b={-3}~~~~~~~~$ [Let's check our work!]